a series of of bank robberies (have , has) occurred during the past several months
Since "of bank robberies" is a prepositional phrase, neither the phrase nor any word in it can be the subject. Therefore, the subject is "series" -- and the word "a" in front of it indicates it's in singular form.
Which of those verbs is also in singular form?
http://grammar.ccc.commnet.edu/grammar/sv_agr.htm
Mrs. Smith need a complete evaluation for her complaint of pain.
His followed the care plan exactly and felt better.
The correct verb to use in this sentence is "has." The subject of the sentence is "a series," which is a singular noun and therefore takes a singular verb form. In this case, since the series of bank robberies is considered as a single entity, we use the singular verb "has."
To determine the correct verb form, you can ask yourself whether the subject is singular or plural. In this case, "a series" is a singular noun, so we use "has" as the present tense singular form of the verb "to have."
Overall, the correct sentence would be: "A series of bank robberies has occurred during the past several months."